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Are the faxes from the same person or different people?
(I have to ask, remember I don't know how much knowledge you have.) If yes, it could be on their end.
Does it do this with copies also? If yes, May be dust on the mirror or
something in the printer getting in the way of the laser.{slight possibility].
How many prints are on the printer? Could be a fuser issue.

set up for fax reception
the following four modes are available for receiving faxes. select a receive mode according to your needs. you can change the receive mode any time. refer to the on screen manual basic guide.
A CALL RING PATTERN DETECTIVE SERVICE (DRPD/NETWORK SWICH) MAY NOT BE AVAILABLE DEPENING ON THE COUNTRY OR REGION OF USE. TEL priority mode- FAX priorty mode- FAX only mode- DRPD/network swich.
press the FAX button then press the MENU button ( the fax setting screen is displayed) use the left or right button to select RECEIVE MODE SET., then press the OK button ( the receive mode set . screen is displayed ) select a receive mode then press the OK button ( the select receive mode is sdisplayed )

You must set the FAX RECEIVE MODE to FAX ONLY. The factory default is FAX/TELEPHONE. You can find the proceedure to change FAX RECEIVE MODE in your owners manual. IIf you don't have an owners manual, try pressing the MENU button, then scroll to one of the following: INITIAL SET-UP, FAX SET-UP, OR FAX RECEIVE MODE. One of these should get you to the FAX ONLY receive mode setting.

Check your preference settings and make sure the fax is set to receive faxes (my friends has 6 different settings) Your manual should tell you how to do this. The default is different for many fax machines.

I think I know why. You need to set the proper priority of your all-in-one Canon device. If it is TEL priority, it means you need to have a phone connected to the fax. If the phone rings, you need to pick up the handset and check if it's a fax tone or a call. If it is fax tone, you wait for 5 secs til fax tone stops, and then hang up. After that you will receive the fax. Failure to pick up the handset will not allow you to receive the fax. This might be the most probable setting you have, hence you can't receive the fax.If it is FAX priority, the same thing happens as TEL priority. Only difference is if you don't pick up, and it is a fax, it will still receive.You can also do FAX only. No need to connect a phone. Device will receive automatically.